Linganisha mbinu

	Kipimo cha Uunganishaji wa Johansen na Kielelezo cha Mfumo wa Kurekebisha Makosa	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Muundo wa Uhusiano wa Kiotomatiki wa Vecta (VAR)
Nyanja	Fedha	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	1991	2001	2015	2005
Mwanzilishi	Søren Johansen	Pesaran, Shin & Smith	Box & Jenkins (Box-Jenkins methodology)	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Aina	Multivariate cointegration / vector error correction model	Cointegration test / Autoregressive distributed lag model	Univariate time-series model	Multivariate time-series model
Chanzo asilia	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.	Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics, 16(3), 289–326.	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Majina mbadala	Johansen test, VECM, vector error correction model, multivariate cointegration	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Zinazohusiana	3	4	5	4
Muhtasari	The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the series and then builds a Vector Error Correction Model (VECM) to describe the short-run dynamics around that equilibrium.	The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains valid whether the variables are I(0), I(1) or a mix of the two, and it is more reliable than Johansen in small samples of roughly 30 to 80 observations.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).